1. Field of the Invention
This invention relates to the method for estimation of the durations for a FINITE DURATION compressible signal to travel from a given transmitting site to a given receiving site through unknown multiple ray paths of all kinds in a given space of practically linear transmission media. More particularly, it relates to a method for improving the performance of the method for estimation of the durations for a given signal to travel between two given points in a given multiple-path signal transmission space using pulse-compression technique.
As compared with the currently popular conventional pulse-compression probing methods which use bandpass signals (typically the chirp) as probing signals and matched filters (or its equivalent cross-correlators) as processors, the aspects of performance improvements are: elimination of side-lobe interference, great enhancement of resolution without need for increase of excitation power/energy, great upgrading of signal-to-noise ratio particularly when the background noise is colored, notably extended probing range, and time-economic data processing. Comparison is made on the bases of employing the same amount of nominal probing signal energy input to the transmitting transducer and using the same basic transmitting and receiving equipment.
The probing signal and the processing mechanism used in the method of the invention are different from those used in the conventional methods. The improvements are particularly remarkable when the traveling times for different paths are crowded and merge into a continuum and/or when the background noise is non-white.
Interesting enough, the method of the invention also features feasibility to safely use transmitting transducer of REDUCED REQUIRED POWER RATING to excite the space yet after processing to eventually yield a VALID required useful output at an unreduced required intensity with simultaneous accomplishment of VERY HIGH RESOLUTION.
The method and system of the invention disclosed herein can be used for seismic geophysical exploration, deep earth crust investigation, earth crust strata movement monitoring, and all kinds of sonic probing including medical probing and mechanical flaw detection. In a more general sense, however, the spirit of method of the invention is ramifiable and applicable to all types of pulse-compression probing applications for estimation of signal travel time that demand elimination of side-lobe problems, high resolution, effective suppression of background noise particularly when it is non-whim, greater probing range at a given excitation energy level, smaller transmitting transducer size, and time-economy in raw data acquisition and processing.
2. From Narrow Pulse Echo Probing to the Use of Long Compressible Probing Signals--The Notion of Equivalent Excitation and the Need for a Narrow Equivalent Excitation
Classically, given the speed of signal wave propagation in a space, sending a narrow enough pulse excitation as a probing signal into the space that contains reflectors and measuring the times elapsed between the instant of transmitting the probing narrow pulse and the instants of arrivals of the reflected waves, one can estimate the distances between the reflectors and the transmit-receive point along the ray paths. With time as abscissa, the recording of reflections to be used for estimating the two-way travel times between the reflectors and the transmit-receive point is referred to as a likeness of the plot of the true impulse response function of the space containing reflectors. The plot of a true impulse response function of the space is the limiting case of a recording of the reflections when the narrow pulse tends to a delta function of time. The true impulse response function of the space is herein denoted as r.sub.o (t). The waveform of the probing pulse is the point-spread-function that blurs the plot of the true impulse response function into an approximate likeness of it. The true impulse response function r.sub.o (t) of a given space manifests the distances between the reflectors and the transmit-receive point and the intensities of the reflections are indicative of the sizes of and the space rates of change of wave impedance at the reflectors interfaces. There is an understanding that due to dispersive transmission characteristic of the media there may exist modification of secondary significance in an r.sub.o (t).
If the narrow exciting pulse is converted from a narrow electric pulse into mechanical excitation through a transmitting transducer and then coupled to the space and the mechanical wave excited in the space after having propagated through the space to the receiving point is picked up and converted back into electrical signal by a receiving transducer, the impulse response functions of these two transducers cascading with the true response function of the space will modify the overall impulse response function. Let us denote the impulse response of the overall cascade as r.sub.o '(t). When we employ both the receiving transducer and also the transmitting transducer, the impulse response functions of the two transducers are both to be sufficiently narrower than required finest details of r.sub.o (t) so that r.sub.o '(t) can reveal the required finest details of r.sub.o (t). In the text to follow, for the sake of referral convenience, let us for the moment assume that r.sub.o '(t) is equal to r.sub.o (t). The effects of the impulse response functions of the transducers on modification on r.sub.o (t) to become r.sub.o '(t) will be given attention to whenever necessary.
The concept of a true impulse response function of a space is naturally and readily generalized to all signal propagation probing problems where there are ray paths of all kinds (paths of direct transmission, refraction and reflection) between the transmitting point and the receiving point with the transmitting point and the receiving point being not necessarily at the same location.
It is the goal of all to procure a likeness of r.sub.o (t) that can best approximate the true r.sub.o (t). The goal demands that we are to make the excitation as narrow as possible to achieve higher resolution. The resolution of a likeness of r.sub.o (t) is a measure defining how refined the details of r.sub.o (t) can be discerned in the likeness.
To procure a useful likeness of r.sub.o (t) in a noisy probing environment there is required an adequate amount of excitation energy. When the excitation pulse is to be narrow, the time rate of release of energy of excitation has to be high. Due to engineering practicing limitations in releasing an adequate amount of excitation energy in a sufficiently short interval, people invoked to the so-called pulse-compression technique, using which the required amount of energy can be released in an elongated time duration.
When a signal is filtered by its matched filter, the signal is reshaped into its auto-correlation function (acf) by the matched filter. The traditional (conventional) pulse-compression technique is based on a fact that for some deliberately designed wideband finite duration signals, the acfs of which have compact central (core) parts that are much narrower than the signals themselves. The time-bandwidth product of the narrow central (core) part of the acf of a signal having such a property is of the order of unity. Such signals are said to be compressible and their respective matched filters are called their respective compressing processors. The acf of such a signal can be called the compressed version of the signal; here a matched filter is used for compressing the compressible signal.
Let us herein denote the general probing signal as x(t). The impulse response function of the matched filter, which is the mirror image of the signal x(t) within a constant multiplier, is x(-t). The acf of x(t), which is therefore x(t)*x(-t) within the same constant multiplier, is denoted acf.sub.x (t). (All in time domain representations.) People want to find signals the center (core) part of whose acf can be slim. Only some sophisticatedly designed signals are compressible by their matched filters.
When the space to be probed is linear, after sending a long compressible signal into the space, collecting the received signal from the space, and processing the collected received signal by the signal's matched filter, what one eventually procures is an output which is the response of the space to an equivalent excitation. The equivalent excitation is the signal after being processed by its matched filter: the acf of the signal. It is the compressed version of the signal.
FIG. 1 explains the notion of the equivalent excitation. FIG. 1-a shows a matched filter probing system in its physical layout: The space which has a true impulse response function r.sub.o (t) (102) is excited by the probing signal x(t) (101). The response of the space to x(t) is x(t)*r.sub.o (t) (104), and it is processed by the matched filter x(-t) (103). The output (104) of the matched filter is therefore ##EQU1## where * stands for convolution operation. From the above expression it is seen that the output of the system is the response of r.sub.o (t) to acf.sub.x (t) which lends itself to playing the role of an EQUIVALENT EXCITATION which excites r.sub.o (t). In FIG. 1-b, relative positions of the space (102) and the matched filter (103) are interchanged relative to that shown in FIG. 1-a. Due to linearity of the space (102) and the matched filter (103), one has the output (104) of FIG. 1-b the same as the output of FIG. 1-a. And FIG. 1-c is the equivalent of FIG. 1-b; in FIG. 1-c, it is shown that the space (102) is excited by an equivalent excitation which is the acf of x(t).
FIG. 1-d is FIG. 1-c with the positions of the block r.sub.o (t) (102) representing the space and the block acf.sub.x (t) (105) representing x(t) compressed by its matched filter interchanged. The output of FIG. 1-d is the same as that of FIG. 1-c. FIG. 1-d shows that the output of a system excited by an x(t) with its output being processed by the matched filter is equal to the output of the system excited by a delta function and post-filtered by a fictitious filter (106) whose time domain characteristic is acf.sub.x (t). The fictitious filter blurs the true impulse response function r.sub.o (t) of the space.
Therefore, when one uses a compressible signal as probing signal and the matched filter of the signal as the compresser, one has: EQU compressed version of the signal x(t)=equivalent excitation=acf.sub.x (t)(2)
with EQU processed output=response of r.sub.o (t) to acf.sub.x (t) (2-a)
or, equivalently, EQU processed output=response of r.sub.o (t) to a delta function, post-filtered by acf.sub.x (t) (2-b)
A matched filter matched to the signal x(t) can be implemented as any linear system which has an impulse response function x(-t), or equivalently implemented by using a linear cross-correlator with its signal input channel being driven by the signal and to its reference input channel being fed a reference input which is the exact replica of the signal x(t) with step-by-step relative shifts.
According to Matched Filter Theory, for any signal of a given energy corrupted by a white noise of a given intensity, the matched filter of the signal processes the sum of signal and noise in such a manner that at the peak point of the signal's acf in the output of the matched filter, the signal-to-noise ratio (SNR) is always maximized to a value which is solely determined by the ratio of the energy of the signal and the power spectral density of the white noise.
We must be cognizant of that the probing information carried by r.sub.o (t) is implicit in the waveform of it: r.sub.o (t) is a time-domain entity. Any linear operator interacting with an r.sub.o (t) must be scrutinized of its behavior in the time-domain to see if it brings about loss of probing information carried by r.sub.o (t) in the time-domain: That is, any equivalent excitation that in effect excites r.sub.o (t) and reveals it as processed output, or any filter that is fictitiously attached to the output end of an r.sub.o (t) and reshapes the impulse response of it, must be examined of its functioning in the time-domain. An operation on r.sub.o (t) that may seem good in keeping energy spectral density function of r.sub.o (t) least hurt does not ensure minimization of loss of information implicit in time-domain. The ultimate judgement of the merit of an equivalent excitation or a fictitious filter is therefore if it can best approximate a delta function of time.
Therefore, seemingly people may say that using a signal which is compressible and using the signal's matched filter to process the signal which is corrupted by white-noise, one can have the happy concordance of two desirable processes: one can simultaneously achieve pulse compression and maximization of SNR at the peak of the processed received signal output.
According to the convolution theorem, when a system is excited by a sufficiently narrow pulse which is narrow enough to reveal the refined details of the system impulse response function, the response of the system to the narrow pulse will approximate the true impulse response function of the system multiplied by the area of the narrow pulse. The slimmer the narrow pulse, the better the response resembles the true response function of the system.
Therefore, if the acf of a compressible probing signal used can be made to asymptotically approach a delta function, the response of r.sub.o (t) to the signal after being processed by its matched filter will correspondingly asymptotically approach r.sub.o (t) of the space multiplied by the area of the slimmed acf. That is, we have, ##EQU2## when width of acf.sub.x (t) tends to be narrower and narrower. This is the philosophy of the pulse-compression approach of procuring a good likeness of r.sub.o (t) by using a compressible long signal and its matched filter.
One can conclude at this point that the key to achieving good performance of pulse-compression approach of estimation of travel times is to find compressible probing signals whose acfs can approach the delta function. People of the detection-ranging profession have been constantly attempting to find compressible signals whose acfs can well approach the delta function.
Regarding the issue of attempting to make the acf of a compressible signal asymptotically approach a delta function of time, we have the following remarks:
A delta function is the limit of a pulse function of a fixed finite area (say, unity area) when the pulse function is time-wise squeezed to make its width tend to zero.
According to Fourier Transform Theory, the area of the acf of a signal is equal to the intensity of the energy spectral density of the signal at zero frequency. Consequently, if the energy spectral density of a signal at zero frequency is zero, the area of the acf is zero.
According to the Matched Filter Theory, the intensity of the acf of a signal at the peak point of it is proportional to the energy of the signal. It is fixed when the energy of the signal is fixed.
3. The Prior Art and Disadvantages of the Prior Art: "Shackled" Resolution, Poor Signal-to-Noise Ratio, and the Side-Lobe Problem
The first finite duration compressible signal conceived by electrical engineers and used in engineering applications was the sweep frequency signal called chirp. It is still the most popular probing signal in use. Pulse-compression probing methods using the chirp as the probing signal is the typical representative of the prior art of pulse compression technique. An example of the auto-correlation function of a chirp is shown in FIG. 2. Being even-symmetrical, it has a central main lobe and a cluster of strong side-lobes flanged around the main lobe. One may have an impression that the sum area of positive lobes and the sum area of the negative lobes of the acf look equal. People had been hoping that the acf of the chirp could have a waveform which could asymptotically approach a delta function. People also hoped that the acf of a chirp could be tuned to contain no protruding sidelobes.
Regretfully, the acf of a chirp cannot be made to asymptotically approach a delta function and the side-lobes of the acf of a chirp are inevitable.
Chirp is a bandpass signal whose energy spectral density at zero frequency can be said to be always zero because the low-frequency end of the sweep cannot reach zero frequency. The energy spectral density function of a linearly swept chirp swept slowly enough almost agrees in shape with the rectangle spanning over the scope of the sweep. Accordingly, one can say that the area of the acf of a chirp is always `zero`. Therefore, the acf of a chirp cannot be made to approach a delta function since it has a `zero` area, and the rippling side-lobes of the acf of a chirp signal are inevitable since there must be ringing side-lobes to add up with the main lobe to a sum which can only be `zero`. To be more specific, as the acf of a chirp is a cluster of ringing lobes compacted around its main or central lobe, the sum area of this core part of the acf compacted around its center is always substantially zero. That is to say, when using chirp as a probing signal, and when the chirp is designed to make the core part of its acf narrow, one has to take into consideration the fact that the area of the core part of the acf is substantially zero. The time width of the main lobe of its acf is of the order of the reciprocal of the frequency sweep width of the chirp and is adjustable by tuning the frequency sweep width. However, making the main lobe (and hence the core part) of acf slim cannot make the acf asymptotically approach the delta function. Therefore, when the signal chirp used to excite the space is so designed that the width of the main lobe of its acf is slim enough for revealing the details of r.sub.o (t), although the response of the space to the chirp after being processed seemingly "may" asymptotically approach r.sub.o (t) in waveform, the INTENSITY of the response inevitably "will" tend to vanish since the area of the acf is `zero` (see Eq.(3)). Consequently, using the signal chirp, there is a limitation that one cannot achieve high resolution.
We can have a complementary explanation to such a situation by using time-domain interpretation. As the acf of the chirp is a slimmed pulse composed of a COMPACTED CLUSTER of ringing lobes which sit close to each other, the equivalent excitation of a system using the chirp and its matched filter has its different component lobe excitations deployed close to each other in time. The response of r.sub.o (t) to the different lobes of the acf would therefore tend to offset each other due to the proximity of the alternately signed different lobes and due to that the areas of the lobes add to zero. The offsetting is more deteriorating for the slower changing components of r.sub.o (t). It is clear that the narrower the whole piece of the acf is, the more refined details of r.sub.o (t) is hoped to be revealed, but the closer the different lobes will be with each other and the offsetting in the general response will correspondingly be more nullifying. Therefore, a probing system using a chirp together with its matched filter has the INBORN WEAKNESS that it cannot ultimately achieve desirable resolution when the energy of excitation is limited. If one wants to use the chirp to achieve a good resolution by designing the signal to make its acf narrow, one has to pay the penalty of greatly increasing the energy of the signal to compensate for the loss of the output due to off-setting of the different lobes of its acf. If, on the other hand, the acf of the chirp is not made to be very narrow, the offsetting will be less nullifying, but the resultant response of r.sub.o (t) to the acf (the equivalent excitation) will be a superposition of responses to its differently positioned blunt lobes. Consequently, the resultant general response can only be a very much distorted likeness of r.sub.o (t). Even so, due to that the areas of the different lobes add to zero, one still has to pay the penalty of greater excitation energy to obtain the much distorted and yet feeble likeness of the true impulse response function of the space. This is the realistic quality of probing systems using the signal chirp.
We can view the zero area problem of the acf of a chirp as that it tends to UNDERMINE the effectiveness of excitation of the probing signal when one attempts to make the processed output better resemble r.sub.o (t) for better resolution even though the composite received signal actually reaching the receiving site has a strong intensity: When r.sub.o (t) has crowded spikes, the composite received wave is processed by the matched filter into so odd a wave that it tends to cancel itself when one tries to tune the chirp for better resolution. Such a mechanism of limitation to achieving resolution can be figuratively called SHACKLING OF RESOLUTION due to the zero area problem of the chirp. To compensate for such shackling of resolution, the energy of the signal is "extorted" to be greatly increased. It is unfortunate for the signal chirp that, although the acf of it is compressible, the cluster of the lobes of the compacted acf has a sum area which is substantially zero.
All bandpass probing signals that have compact acfs with compacted clusters of rippling lobes have in common the problem of acf area self-offsetting due to diminished energy spectral densities at zero frequency. They all have the difficulty in achieving resolution at an un-extorted excitation energy level.
Historically, pulse-compression reflective probing using the signal chirp as probing signal and its matched filter as compressing processor was contemplated simply for probing spaces containing only thin reflectors that are very sparsely separated. In such cases one does not have the need for a really narrow and single-lobed acf. What people primarily concern about is if they can detect the presence of the sparsely separated thin spikes with maximized SNR and can thence well estimate/locate the time positions of the thin spikes. In such cases the signal chirp works unblemishedly in spite of that its acf has out-stretched flange and side-lobes and that the area of the acf is zero.
However, when there are spikes crowded together or blocks of merged up spikes in r.sub.o (t) (for example, in reflection cases, when there are crowded reflectors such as it is in the case of geophysical exploration, or when there are slanting reflectors of large longitudinal sizes), there would be the requirements that the acf of the signal SHOULD BE NARROW ENOUGH, does not have side-lobes, and that the area of the acf does not equal to zero. An out-stretched flange with side-lobes will obscure the discernibility of the individual spikes and make the desirable optimal SNR quality of the matched-filter pulse-compression method badly invalidated: There will be garbling of the true impulse response function and SNR degradation. These are due to that the icons of the acfs due to neighboring spikes in r.sub.o (t) will mutually smear. Mutual smearing gives rise to garbling (mutual masking) of the different icons of the acfs pertaining to neighboring spikes in r.sub.o (t), and SNR can no longer be maximized because of the randomness of mutual smearing due to out-stretched flanges of icons of neighboring acfs of random strengths. The more densely the individual spikes of r.sub.o (t) of the space are crowded, the more acute will be the mutual masking of the icons of the acfs of neighboring spikes of r.sub.o (t) and the more forbidding will be the degradation of SNR.
Therefore, when r.sub.o (t) has crowded spikes, not only the zero-area problem would harm SNR and shackle resolution, but also the side-lobes and out-streteching flanges of the acf would incur garbling of r.sub.o (t) and degradation of SNR due to mutual smearing of the neighboring spikes of r.sub.o (t).
As a typical example, in the case of seismic geophysical prospecting, the spikes in r.sub.o (t) are often so densely crowded that they form a continuum. There are superposed slow and fast ups and downs in r.sub.o (t)s. In such cases, a probing system using the chirp and its matched filter CAN NEVER achieve desirable resolution and SNR performances in any sense due to the reasons explained above.
Here, we can have a comment on the problem of limited resolution performance of the chirp and matched filter method in seismic geophysical exploration cases. According to the above, it is chiefly the problem of "shackled resolution" which is in force that limits resolution: When people boost the high frequency end of the chirp signal to attempt accomplishing better resolution, people go more entangled in the zero area problem of its acf. Unfortunately, it has been mis-judged that the limited resolution achievable in employing the chirp and matched filter method in seismic geophysical prospecting is due totally to the limitation to transmission of probing signal at high frequency end of the passband of the earth. As a matter of fact, using very large number of small dosage dynamite detonation excitations of slimmer width and stacking the very numerous feeble received waves, people have succeeded in obtaining the likeness of an r.sub.o (t) with relatively satisfactory resolution. The small dynamite dosages imply slimmer excitation pulses. They carry high frequency probing signal components, and they characterize relative freedom from out-stretched flanges and rippling side-lobes which the acf of chirp signal has. It is the high frequency components of the small dosage detonations that help upgrade resolution. Although the high frequency end of the passband of the earth does attenuate high frequency components of the probing signal, a slim excitation does let reflections better tell the true story of the transmission medium. From such a fact we can appreciate the importance of getting rid of the zero area problem of the acf of a probing signal when r.sub.o (t) has crowded spikes that merge up. For the case of seismic geophysical exploration using method with chirp as probing signal and its matched filter as compressing processor, when it is needed that desirably high resolution be achieved, the needed increase of probing energy can be tremendously great such that the transmitting transducer is colossally bulky, and such a need for giant transmitting transducers has currently become a forbidding stumbling block to wider employment of the conventional probing method using chirp/matched filter. On another side, the increase of probing energy suggests the probed space/object is over-agitated than it actually is needed to be energized, and this is not desirable at all.
Now one sees the unhappy and gloomy aspects of the probing method using the signal chirp with its matched filter: compelling side-lobes, inborn low SNR, and doomed poor resolution, when the spikes of arrivals in r.sub.o (t) are not sparse and not thin.
More, when the background noise is non-white, the matched filter, which has for its impulse response function the image of the probing signal, cannot process the signal plus noise to attain a maximized SNR at the peak points of the processed output even if the spikes in an r.sub.o (t) are sparsely scattered and thin.
Readers interested in the chirp signal and matched filter method are referred to, for example, J. R. Klauder et al: Theory and Design of Chirp Radars, Bell System Technical Journal, vol. 39, pp 745-808, July, 1960. The reader is also referred to P. L. Goupillaud: Signal Design in the Vibroseis Technique, Geophysics, vol. 41, pp 1291-1304, 1976.
4. A Simple Approach to a New Horizon
Workers of the pulse-compression detection-ranging profession have been very diligent in attempting to find finite duration compressible signals whose acfs can be narrow, without side-lobes, and can approach the delta function really well. Of course people also want the matched filters of such signals to be capable to effectively suppress background noise when it is non-white. Regretfully, none succeeded.
Aiming at eliminating side-lobes, some workers of the seismic geophysical prospecting industry had been attempting to make use of the property of being free from side-lobes of the acfs of CYCLICALLY REPETITIVE m-sequences in designing good finite duration probing signals. Some aspired that the acf of a finite duration signal formed by coding BANDPASS pulses by a single period m-sequence might be tuned to be free from side-lobes. Again regretfully, none succeeded. They all used the matched filter to reshape the probing signal into its acf for pulse-compression: They all used the REPLICA of the probing signal as reference signal to obtain the signal's auto-correlation function which plays the role of equivalent excitation. Basically, they used a single period m-sequence to code a sinusoid/cosinusoid to form the finite duration probing signal wherein the bit duration of the m-sequence had to be an integral multiple of the period of the sinusoid/cosinusoid while the frequency of the sinusoid/cosinusoid was to be located in the middle portion of the earth's apparent bandpass transmission passband. Since the auto-correlation function (acf) of a single-period m-sequence cannot be free from side-lobes, the side-lobe elimination problem could not be resolved as desired. Since the acf of a sinusoid/cosinusoid coded by an m-sequence whose bit duration is limited to be no narrower than the inverse of a frequency which is located in the midband of the earth's transmission passband and cannot be high, the central (core) part of the acf cannot be made narrow and hence resolution problem and mutual smearing problem in seismic geophysical prospecting could not be resolved. Since the energy spectral density function of coded band-pass wavelet strings can only have very much diminished intensities at zero frequency, the problem akin to the zero-area problem explained above could not be escaped and hence the methods could only achieve poor SNR at un-exaggerated excitation energy levels and "shackled" resolution. Since in seismic geophysical prospecting the background noise picked up at the receiving site is always non-white and has a pass-band which often closely coincides with the pass-band of the probing signal, the background noise cannot be effectively filtered out by the processing filter. As a result, the performance of their methods had proved to be practically no better than the currently prevalent method of using chirp as signal and its matched filter as the compressing processor, and could not come in to popular use. A representative report on field experience of said attempts can be found in A. B. Cunningham: Some Alternate Vibrator Signals, Geophysics, Vol. 44, p. 1901 ff, N.sup.o. 12, December, 1979. Other typical examples of finite duration probing signals attempting to apply m-sequence to signal design in seismic geophysical applications can be found in U.S. Pat. No. 3,264,606 to T. N. Crook et al, and U.S. Pat. No. 2,234,504 to C. R. Wischmeyer.
Fortunately, by using a LOW-PASS wavelet in place of using a BAND-PASS wavelet as the elementary wavelet of the string of wavelets which are amplitude-coded by the single period of the m-sequence in the probing signal, by using a special reference signal which is based on a cyclical repetition of the same m-sequence in place of using the simple replica of the probing signal as the reference signal, and by insightfully exploiting the working principle of the above stated method using the attributes of m-sequence by trickily imposing a TEMPORAL-NARROWNESS REQUIREMENT on the parameters of the probing signal, all the undesirable drawbacks of the conventional pulse-compression probing methods are removed. INTERESTING ENOUGH, based on an unobvious but sound rationale, the POWER RATING of the transmitting tranducer can be REDUCED when the special temporal-narrowness requirement on the probing signal parameter is met.
By making the above changes in probing signal design and reference signal formation, the equivalent excitation can be made to be free from zero-area problem, DESIRABLY and NOTABLY SLIM, free from out-stretching flanges, and free from side-lobes, and we come up to the method of the invention. As consequences of having the many drawbacks of the conventional method of pulse-compression remedied as based on the above listed qualities, the method of the invention features greatly upgraded resolution, greatly enhanced SNR, notably extended effective probing range, freedom from garbling of r.sub.o (t), relief from need for increased excitation power/energy for upgrading resolution, and in addition, the feasibility of using transmitting transducers of lighter weight when the temporal-narrowness requirement is met. The method of the invention also has the capability of minimizing processed background noise when the original background noise is colored. The method of the invention is time-economic in field data aquisition and processing computation.
We will see that the method of the invention opens a door to a new horizon. The method of the invention does not require sizable new equipment to be built, and its performance has been field tested and reported (without disclosing the method) in Hong-Bin Chen and Neng Eva Wu: A New Result in the Method of Seismic Data Acquisition, Society of Exploration Geophysicists (SEG) Annual Meeting Expanded Abstract Book, 1988, Anaheim. The reported results fully substantiate theoretical prediction. The reported results advocate that meeting the temporal-narrowness requirement will result in achieving expected performances. The mechanisms that achieve the many improvements will be explained in the SUMMARY OF THE INVENTION and THE DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT OF THE INVENTION in the text to follow.